Looking to Load and Resistance Factor Rating

by Becky Jaramilla and Sharon Huo

The LRFR process aims to improve the reliability of bridges and increase public safety.

On December 15, 1967, the Silver Bridge, carrying U.S. 35 between Point Pleasant, WV, and Gallipolis, OH, collapsed, killing 46 people and injuring 9 when 31 of the 37 vehicles on the bridge either fell into the Ohio River or onto its shoreline. Investigations later revealed that a cracked eyebar created undue stress on the other bridge members, leading to the collapse.

These inspectors are using a truck-mounted boom to collect data needed to determine the bridge’s load carrying capacity.

The incident prompted national concern about bridge conditions and led to the establishment of the National Bridge Inspection Standards (NBIS) in the early 1970s. Since then, the Federal Highway Administration (FHWA), the American Association of State Highway and Transportation Officials (AASHTO), and others have worked to improve standards for maintaining and inspecting existing bridges. The latest major effort in this area is the development of the load and resistance factor rating (LRFR) method. In 2001 AASHTO adopted a new Guide Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges. The guide manual reflects the most current technologies and builds on the structural reliability approach inherent in specifications for load and resistance factor design (LRFD).

These inspectors are using a truck-mounted boom to collect data needed to determine the bridge’s load carrying capacity.

All States are working to implement LRFD fully by October 2007, as decided by AASHTO and agreed upon by FHWA. As States adopt LRFD across the country, bridge professionals are recognizing the need for a methodology for rating the load carrying capacity of existing bridges that is consistent with the load and resistance factor philosophy. Although the LRFD specifications focus on the design of bridges, LRFR takes a parallel track aimed at determining the load ratings for inservice bridges.

LRFD and LRFR introduce the United States to an innovative philosophy that is consistent with major bridge design codes in Asia, Canada, and Europe. Based on factors calibrated from structural load and resistance statistics, the LRFD specifications ensure a more uniform level of public safety and reliability in newly designed bridges. Ultimately, bridge engineers expect that the LRFD/LRFR approach will help reduce maintenance and repair, avoid costly overconservative designs and ratings, and result in a more uniform level of public safety on bridges in the United States.

Permit load rating calculations resulted in the safe transport of this truck, which exceeded the State’s legal load and size limit.

Overview of Load Rating

Bridge design and load rating are similar in overall approach; however, they differ in one crucial aspect. In design, engineers contend with greater uncertainty in the amount of loading the structure will experience over its service life. With load rating for an existing structure, on the other hand, bridge engineers face uncertainty in the amount of structural resistance.

In general, load rating involves determining the safe carrying capacity. Bridge owners perform three types of load rating: design, legal, and permit. Design and legal load rating involve the analysis of routine loads that are within the legal limits. Permit load rating is the analysis of specific vehicles that carry loads that are heavier than the legal limit.

Bridge owners perform load ratings for three main reasons:

Modern bridges generally are constructed to last at least 50 years, and some even longer. Even with proper maintenance, however, the condition of a bridge inevitably will deteriorate to some extent over its lifetime. This deterioration could lead to a reduction in the strength or load carrying capacity of the bridge. To ensure that all public bridges remain safe under current traffic loads, load-rating analyses must be performed when bridge conditions deteriorate. According to the NBIS, owners need to collect condition data for all public bridges on a 24-month cycle.

Bridges in the current inventory were designed using a variety of configurations for live truckloads, depending on the design specifications at the time the bridge was built. As design and rating specifications evolve, new knowledge of actual loading, behavior, and resistance are incorporated. Therefore, regardless of the design methods used, all bridges should be load rated using current traffic conditions and the latest standards, whenever practicable, to ensure the safety of the motoring public.

Lastly, a permit load rating is necessary for vehicles carrying loads over the legal limit. Due to increasing demands on the trucking industry, the volume of requests for permit load ratings continues to rise, according to the Bureau of Transportation Statistics. Heavy or frequent permit loads can reduce a bridge’s life or cause permanent structural damage if not assessed properly.

For load rating, results are generally expressed in terms of a rating factor for a particular live load model. Rating factors greater than one indicate that the bridge is safe for the loads tested. Currently there are three methods available for load rating bridges: allowable stress rating, load factor rating, and LRFR.

Historical Background Of Load Rating

In the 1950s and 1960s, construction of the U.S. interstate system and State highway systems was progressing at an extraordinary rate. According to the Bridge Inspector’s Reference Manual (FHWA-NHI-03-001), approximately 115,000 public bridges in the United States were designed and built between 1961 and 1970. During this time, highway officials placed little emphasis on safety inspections and maintenance of inservice bridges.

After the collapse of the Silver Bridge in West Virginia in 1967, the U.S. Congress responded to the public outcry by directing the secretary of transportation to establish national standards for bridge inspection. In 1971, when the NBIS was created, they only applied to bridges on the Federal-Aid Highway System (generally bridges on any interstate, U.S route, or State route system). Later, in 1980, FHWA extended the standards to cover all public bridges more than 6 meters (20 feet) in length. The NBIS established a national policy on inspection procedures, frequency, personnel qualifications, reports, and maintenance of the National Bridge Inventory (NBI).

The AASHTO Manual for Maintenance Inspection of Bridges, released in 1970

The FHWA Recording and Coding Guide for the Structure Inventory and Appraisal of the Nation’s Bridges, released in 1972

The NBIS established directives not only for inspecting bridges but also for evaluating and analyzing the observed condition of bridges. Determination of load capacity or load rating is a key component in the evaluation of condition data gathered during inspections.

Detailed procedures for load rating first appeared in the AASHTO Manual for Maintenance Inspection of Bridges. The specifications provided a nationwide, unified approach to load rating. In the late 1980s, however, the bridge community identified a number of shortcomings in the specifications. For example, inspectors arrived at a wide range of results for load ratings on similar bridges. AASHTO officials determined that the disparities were mainly due to variation in interpretation of the load rating specifications.

To improve the procedures, in 1989 AASHTO released the Guide Specifications for Strength Evaluation of Existing Steel and Concrete Bridges, providing the first version of the LRFR procedures. By using the safety reliability approach outlined in the guide, engineers found that the load calculation results were more convergent. The guide specification also provided the option of using site-specific traffic information and the structural behavior history of the bridge to arrive at more accurate results. At that time, however, State departments of transportation (DOTs) were still using load factor design or allowable stress design, so adopting LRFR was not an attractive option for many States.

In 1994, AASHTO published the Manual for Condition Evaluation of Bridges to replace the Manual for Maintenance Inspection of Bridges. Although the new manual contained some guidance for allowable stress rating, it clearly emphasized load factor rating. Because most designers were then using load factor design, the load factor rating method was the logical and preferred system for rating bridges. In addition, FHWA released a 1993 policy memorandum requiring all States to report annual load rating data using the load factor rating method by 1994 for new or repaired bridges and by 1995 for all existing bridges. Therefore, since the early 1990s, load factor rating has been the primary load rating method used across the United States.

The AASHTO Bridge Subcommittee voted to adopt the LRFD specifications for bridge design in 1993. Then in 1998, AASHTO identified LRFD as the primary design specification for highway bridges.

Since that time, many States have fully or partially adopted LRFD as their primary method for designing bridges. With the advancing deadline for implementation of LRFD, AASHTO recognized the growing need to further develop LRFR specifications and update much of the Manual for Condition Evaluation of Bridges. In response, AASHTO released the 2003 Manual for Condition Evaluation and Load Resistance and Factor Rating of Highway Bridges.

The guide manual represents a major overhaul of the earlier Manual for Condition Evaluation of Bridges. All but two of the sections were entirely rewritten. Although the manual emphasizes the LRFR method, it provides rating procedures for both load factor rating and LRFR to allow States the option of rating their existing inventory with either method. The manual includes numerous examples to demonstrate the use of the LRFR method. In addition, customized load factors for overload permit review and new sections on fatigue evaluation and nondestructive testing are among some of the other enhancements. As with the earlier guide specifications, the new manual applies state-of-the-art technology and allows the use of site-specific traffic and structural behavior conditions.

As noted in NCHRP Web Document 28 (Project C12-46): Contractor’s Final Report: Manual for Condition Evaluation and Load Rating of Highway Bridges Using Load and Resistance Factor Philosophy, the LRFR methods presented in the 2003 manual “contain the necessary ingredients to provide a more rational, a more flexible, and more powerful evaluation strategy for existing bridges.”

Load Factor Rating

The load factor rating method rates bridges at two levels: inventory and operating. The inventory rating level corresponds to customary design-type loads while reflecting the existing condition of the structure. The operating rating level corresponds to the maximum permissible live load the structure can withstand safely. Further, the inventory load rating accommodates live loads that a bridge can carry for an indefinite period, while the operating load rating refers to live loads that could potentially shorten the bridge life if applied on a routine basis.

As stated in the AASHTO Manual for Condition Evaluation of Bridges, the general expression used in load factor rating calculations is as follows:

In the equation, RF is the rating factor for live-load carrying capacity, C is the capacity of the structural member, D is the dead-load effect on the member, L is the live-load effect on the member, I is the impact factor, A1 is the factor for dead loads, and A2 is the factor for live loads. The dead-load factor (A1) equals 1.3 for all rating levels, and the live-load factor (A2) equals 2.17 for inventory level and 1.3 for operating level.

Capacity (C) is calculated as outlined in the AASHTO Standard Specifications for Highway Bridges. The structural layout and materials determine the capacity. For load rating, capacity depends on the present condition of the structural components. Therefore, engineers need to account for observations such as cracked or deteriorated sections when performing capacity calculations.

In load factor rating calculations, dead loads (D) are permanent loads that do not change as a function of time. Generally, for bridges, dead loads include self weight and any permanent external loads. Live loads are temporary loads that act on a structure. As defined in the AASHTO Standard Specifications for Highway Bridges, the design live load is defined as H20/HS20 truck loading or lane loading using the load that produces the largest moment or shear. AASHTO established the H20 and HS20 trucks as standard live-load models to facilitate a simpler analysis based on an approximation of the actual live load; they are not meant to represent actual vehicles. Similarly, standard lane loading provides a simple method for calculating a bridge’s response to a series of trucks. Bridge owners also can calculate the distribution of live load to a single structural member as outlined in the AASHTO specifications.

The load factor rating design loads do not adequately represent current loads on the highways and do not provide a uniform safety level for various bridge types and span lengths. Therefore, legal load calculations are commonly used to ensure the structural integrity of public bridges. Three AASHTO legal loads produce controlling moment and shear reactions for the short, medium, and long spans respectively. In addition to AASHTO legal loads, many State DOTs have State-specific legal loads that are used in load rating calculations.

Bridge owners also can check permit loads using load factor rating when they receive requests for overload permits. In permit load rating, the weight and dimensions of the actual truck should be used in place of the AASHTO load models.

The load factor rating impact factor (I) is added to all live loads to account for the speed, vibration, and momentum of vehicular traffic. The AASHTO specifications for bridge design define the impact factor as follows:

After determining the rating factor for a structural member, the bridge owner then multiplies the rating factor by the weight of the live load truck to yield the bridge member rating for that member. The overall rating of the bridge is controlled by the structural member with the lowest rating.

Load and Resistance Factor Rating

As with load factor rating, bridge owners can calculate load ratings on both operating and inventory levels using the LRFR method. In addition, LRFR uses limit states for strength, service, and fatigue to ensure safety and serviceability in the load rating. These limit states were introduced in the AASHTO LRFD specifications. The strength limit state accounts for the strength capacity of the structure under permanent and live loading. The service limit state accounts for stress, deformation, and crack width. The fatigue limit state accounts for cyclical stress ranges to avoid fatigue cracking. Strength is the principal limit state and, therefore, is the main determinant for bridge posting, closing, and repair. Both service and fatigue limit states can be applied selectively to bridges.

As stated in the AASHTO Manual for Condition Evaluation of Bridges, the basic LRFR equations are as follows:

In the equations, RF is the rating factor, C is the structural capacity, Rn is the nominal member resistance (as inspected), DC is the dead-load effect of structural components and attachments, DW is the dead-load effect of wearing surfaces and utilities, P is the permanent loading other than dead loads, LL is the live-load effect, IM is the dynamic load allowance, DC is the LRFD load factor for structural components and attachments, DW is the LRFD load factor for wearing surfaces and utilities, P is the LRFD load factor for permanent loads other than dead loads, L is the evaluation live-load factor, c is the condition factor, s is the system factor, and f is the LRFD resistance factor.

Nominal resistance (Rn) is the ability of the bridge to withstand applied loads. Resistance must be calculated to determine the capacity of the bridge. For load rating, resistance depends on the structural layout, bridge material, and the present condition of the structural components. After determining the nominal resistance, a bridge owner can calculate the capacity by applying the product of the three safety factors: , c, and s. The resistance factor () is the same factor used in LRFD bridge design and accounts for the general uncertainties of a bridge member in satisfactory condition. The condition factor (c) is used to account for increasing uncertainties in a bridge member once its condition deteriorates. The condition factor is equal to 0.85 for members in poor condition, 0.95 for members in fair condition, and 1.0 for members in good condition. The system factor (s) accounts for the level of redundancy in the structure. Bridges that are less redundant or nonredundant will be assigned a lower system factor and therefore will have reduced calculated capacities.

In LRFR calculations, permanent loads are separated into the three variables DC, DW, and P, because each is assigned an independent load factor () for each load rating limit state. All permanent loads are calculated in accordance with the bridge conditions at the time of the analysis. Load factors for permanent loads and live loads are specified in the AASHTO Guide Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges.

As with load factor rating, LRFR live loads are temporary loads that act on a structure. Vehicular loads are the primary live loads that affect bridges. For nonpermit load rating, the LRFR system is a tiered approach. The bridge owner performs an initial check based on the HL-93 design load at the applicable design limit states. As with H20/HS20 loading, AASHTO established HL-93 as a standard model for live loads, so it does not represent an actual vehicle. The HL-93 load model under the LRFD methodology is equivalent to the H20/HS20 model truck in combination with the HS20 uniform lane loading. The load rating equation has been calibrated such that if a check of the design load yields a satisfactory load rating, then the bridge owner can assume that the bridge will yield satisfactory load ratings for all AASHTO legal loads. Therefore, an inventory design load rating resulting RF >1 requires no further legal load analysis.

Bridge owners generally perform legal load rating only as a second-level evaluation when HL-93 loads exceed the bridge capacity. Legal load rating provides the load capacity of any of the AASHTO or State models for legal load. (Note: If States develop their own legal loads, owners need to perform an analysis to ensure that the State-specific loads are enveloped within the HL-93 design load.)

Inspectors deemed this bridge closure necessary based on a load rating calculation.

Finally, owners perform permit load rating only for vehicles carrying loads that exceed the legal limit. Permit procedures apply only to bridges that have adequate capacity to carry design or legal loads. In permit load rating, the weight and dimensions of the actual truck should be used in place of the AASHTO load models.

Calibrating LRFR

When calibrating any design or evaluation code, engineers develop a procedure to account for structural reliability or, conversely, the probability of failure. The LRFR, like the LRFD code, bases this reliability on the safety index () system, where, as described in the National Cooperative Highway Research Program’s NCHRP Report No. 454: Calibration of Load Factors for LRFR Bridge Evaluation, is defined as follows:

Safety Index, = mean value of g
Standard deviation of g

g = Resistance - Dead Load - Live Load + Impact

As the equations indicate, large positive values for g (a positive value indicates a safe element) and/or small values for the variation of g will yield a higher safety index. Higher safety indices mean higher reliability. Safety indices provide a measure of the structural reliability or, conversely, the risk that a design component has inadequate capacity in a given limit state.

Selecting a target b is based on economics. Increasing the safety index can lead to costly overcon-servative design and evaluation, while decreasing the safety index can lead to expensive maintenance or replacement of failed components. For LRFD, the target safety index chosen was b equals 3.5. Assuming a normal distribution, this safety index ensures that during the design life of the structure, only 2 out of 10,000 components will experience loading that exceeds the component’s resistance, as FHWA’s Myint Lwin noted in the article “Why the AASHTO Load and Resistance Factor Design Specifications?” published in 1999 in Transportation Research Record #1688.

The LRFR target safety index is b equals 2.5 at operating level and equals 3.5 for inventory level. The operating safety index of equals 2.5 ensures that only 6 out of 1,000 components will experience loading that exceeds the component’s resistance. The operating reliability can be justified on many grounds, including the fact that the exposure period for evaluation is much shorter (2 to 5 years between inspections) compared to the 75-year exposure period for design. In addition, the relative cost for increasing the safety index during the evaluation phase is much higher when compared to the cost of increasing the index during the design phase.

The load and resistance factors , c, s, DC, DW, and L are calibrated using the selected safety index targets to achieve uniform safety for all material types, spans, and load effects.

Because the LRFR live-load factors depend on average daily truck traffic (ADTT), researchers used traffic data for calibration. They used weigh-in-motion data from sites with ADTT values of at least 5,000 to determine the probability of side-by-side heavy vehicle events. The researchers used the field data in a traffic-flow model to interpolate probability values for other ADTT values.

Understanding the Advantages

To enable a smooth transition from load factor rating, the LRFR research team set a goal to make the manual practical and easy to use. “Although some bridge owners may think that it will be more difficult to use, LRFR is actually as easy, if not easier, to use than LFR,” says Firas Ibrahim, senior bridge codes and specifications engineer at FHWA.

The load and resistance factors are calibrated to account for the safety reliability, so this aspect remains invisible to the evaluator. In addition, loading procedures were designed to appear to be an extension of the current load factor rating method.

As with LRFD, LRFR promises a more uniform level of safety and a lower risk of over- or underdesigned members. The LRFR approach can lead to a decrease in costly traffic restrictions and bridge strengthening or repairs as well.

Although the general equations are similar for the current LFR and new LRFR methodologies, and the procedures are straightforward, the implementation of a new load rating method can be time-consuming and costly for State DOTs. Nevertheless, the following is a list of credible reasons to justify adopting the new LRFR procedures.

LRFR provides a simplified approach through the use of the HL-93 live loading as a screening check for all other legal loading. Previously, with LFR, the HS20 truck did not represent current highway conditions and did not provide uniform reliability over varying span lengths. To achieve reliability, States applied load factor rating to three separate AASHTO legal load models, with each one controlling short, medium, or long spans respectively. Only the combined use of the three AASHTO legal loads resulted in uniform reliability. With LRFR, the HL-93 can achieve this uniform reliability for all span lengths with only one load combination.

LRFR enables bridge owners to apply traffic volume and other site-specific data when determining live-load factors for a bridge. If more information is available, such as truck loads through weigh stations, evaluators may take a more refined approach by estimating site-specific load factors that are characteristic to the bridge site. This procedure could be especially advantageous to bridges carrying light truck traffic.

LRFR facilitates using the past performance of a bridge to help determine its serviceability rating. If inspectors find no problems with past performance, restrictive load posting based on calculated serviceability performance measures may not be justifiable. In cases like this, evaluators can use past performance as a proof test for serviceability.

LRFR describes procedures for nondestructive load testing, which involves field observations and measurements of inservice bridges. Because bridge ratings tend to be fairly conservative, field load testing often can reveal additional capacity, as noted by Michael Barker in “Quantifying Field-Test Behavior for Rating Steel Girder Bridges,” published in the July/August 2001 issue of the Journal of Bridge Engineering.

Lastly, the NCHRP Project C12-46 reported that in trial load ratings “DOT rating engineers were able to perform the LRFR evaluations without undue difficulty and with relatively few errors.” This finding demonstrates that bridge evaluators do understand the procedures and that implementation is feasible.

“Bridge owners need a rating methodology that produces results that are closer to reality, not closer to prior rating methodologies,” says Ibrahim. “The LRFR methodology provides a reality check and produces meaningful, reliable results that are superior to those of prior rating methodologies.”

Field Trials and Comparisons

While developing the new LRFR manual, NCHRP researchers compared LRFR and load factor ratings on several actual bridges representing various types and physical conditions. Evaluators performed ratings at both inventory and operating levels under design and legal loads and presented their results for three groups of bridges: steel multigirder, reinforced concrete T-beam, and prestressed concrete I-beam bridges.

For steel multigirder bridges, LRFR design inventory ratings were slightly lower than load factor rating bridges. Lower ratings indicate a more conservative result and lower allowable loading. LRFR design operating ratings were lower than load factor rating. The LRFR legal load ratings were higher than inventory ratings and almost equivalent for operating ratings using the load factor rating method. The researchers also performed trial ratings on nonredundant steel bridges but determined that the number of bridges studied was too small to permit drawing any conclusions.

For reinforced concrete T-beam bridges, LRFR design load ratings were lower than those achieved using load factor rating for both inventory and operating levels. Legal load ratings for LRFR were higher than those for load factor rating for inventory but lower for operating.

The results for prestressed concrete were more widely scattered than those for steel or reinforced concrete. The majority of load ratings achieved using the LRFR approach for the prestressed concrete bridges were governed by shear rather than flexure stresses, which is a substantial difference from the load factor rating method where flexural ratings typically govern for all bridge types. The researchers attribute the reversal due to a number of issues. For the design limit state, the LRFR HL-93 loading causes higher shear stress than the HS20 loading. In addition, the shear distribution factors are higher using the LRFR method. Most importantly, the evaluators used the modified compression field theory to calculate shear resistance instead of the previous semiempirical formula.

For prestressed concrete, the results generated through the modified compression field theory can be very different than those for load factor rating. However, in accordance with the AASHTO Guide Manual for Condition Evaluation and Load and Resistance Factor Rating (LRFR) of Highway Bridges, inservice concrete bridges that show no signs of shear distress do not need to be checked for shear when rating for design or legal load. (Evaluators still need to check shear for the permit load rating.)

Moving Toward Implementation

To date, several States have either fully or partially adopted LFRD as their primary design method for bridges. Few States, however, have adopted LRFR as their primary method for load rating. A recent survey of 32 States showed that 15 have used LRFR in only sample load rating. Because the methodology of LRFR is synonymous with LRFD, advancing the implementation of the latter will help with the eventual adoption of the former. Additional sample ratings, training, and research can help the bridge engineering community gain the confidence it needs to fully implement the new LRFR method across the United States. “Although States and other bridge owners may be cautious about embracing this new approach,” says Ed Wasserman, director of the structures division at Tennessee Department of Transportation (TDOT), “we understand that LRFR offers an apparent improvement in reliability and uniformity when rating bridges. We expect that any issues will be overcome with time.”

The map shows the status of LRFD implementation across the United States as of April 2004 (the latest date for which information was available at the time of publication). Source: FHWA.

The recently released LRFR software that works with the popular computer-based tool Bridge Rating and Analysis of Structural Systems or BRASSTM should help ease the concern among States about the time and effort that will be invested in switching to LRFR. As State DOTs move through the process of implementing LRFD and LRFR, FHWA staff members are available for technical assistance and consultation.

Goodrich, B.L. and Puckett, J.A. “Comparison of LFR and LRFR for Concrete Bridges,” Proceedings from the 2002 Concrete Bridge Conference, sponsored by FHWA and the National Concrete Bridge Council, Nashville, TN, October 6-9, 2002.

Becky Jaramilla, P.E., presently serves as the assistant bridge engineer in the FHWA Tennessee Division Office. Her role covers all aspects of bridges, including design, construction, and inservice inspection. Jaramilla holds a professional engineering license in Tennessee. She has a B.S. in engineering from the University of Illinois at Chicago and is currently working towards an M.S. in civil engineering at Tennessee Technological University.

Sharon Huo is an associate professor in the Department of Civil and Environmental Engineering at Tennessee Technological University. She holds a Ph.D. from the University of Nebraska and has 13 years of experience in structural analysis and design. Her research specialties include the behavior of prestressed concrete members, live load distribution in bridge design, and bridge analysis and rating. She is a registered professional engineer in Nebraska.

The load and resistance factor design and rating of structures is one of the FHWA priority, market-ready technologies, which are innovations that have proven benefits and are ready for deployment (see www.fhwa.dot.gov/crt/lifecycle/ptisafety.cfm).